'You'd think the one thing a computer would be good at was sorting classes and putting them in the right rooms. All it requires is logic,' said Braintree, Head of English.
'Logic, my foot.Try using logic with Mrs Robbins who won't teach in Room 156 because Laurence Seaforth is next door in 155 and she can't make herself heard for the din his drama class makes...'

"you would think", as you say, is stronger. It means "It should be this way." Generally, it's used to say "It should be this way, but it isn't"

"You'd think Brits and Americans would be able to understand each other." would literally mean "Brit's and Americans should be able to understand each other." And would normally imply "But they don't understand each other."